More precisely, we let \({\Delta {T}\mathrm {op}}\)  denote the category of \(\Delta \) -generated topological spaces (see [1]}, [2]} for background).
We will be working with \({\Delta {T}\mathrm {op}}\)  as our choice of category of topological spaces throughout; however, most of the theory in this paper also works with the category of Kelley spaces (see, for instance, [3]}), except for where we work explicitly with diffeological spaces (Lemma REF , Remark REF ).
